What is the integral of 12sqrt(x)+4 ?

The integral of 12sqrt(x)+4 is 8x^{3/2}+4x+C

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integral of 12sqrt(x)+4

\int 12 x + 4 d x

8 x^{\frac{3}{2}} + 4 x + C

Solution steps

\int 12 x + 4 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 12 x d x + \int 4 d x

\int 12 x d x = 8 x^{\frac{3}{2}}

\int 4 d x = 4 x

= 8 x^{\frac{3}{2}} + 4 x

Add a constant to the solution

= 8 x^{\frac{3}{2}} + 4 x + C

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What is the integral of 12sqrt(x)+4 ?
The integral of 12sqrt(x)+4 is 8x^{3/2}+4x+C